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Math Help - expected value and variance

  1. #1
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    expected value and variance

    okay I am having some issues (i think) withthe expected value and variance of my PDF.

    Let me see if I have it right.

    My pdf is 2/(x^3) from 1 to 2000.



    I get my mean to be 2 and my expected value and variance-graph.jpeg
    variance to be 2 log(2000)-4. Is that correct? If you look at the graph it doesnt seem to be right (the mean is the right solid red bar.) maybe it is because it just extends so far?
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  2. #2
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    Quote Originally Posted by xamius View Post
    okay I am having some issues (i think) withthe expected value and variance of my PDF.

    Let me see if I have it right.

    My pdf is 2/(x^3) from 1 to 2000.



    I get my mean to be 2 and my Click image for larger version. 

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    variance to be 2 log(2000)-4. Is that correct? If you look at the graph it doesnt seem to be right (the mean is the right solid red bar.) maybe it is because it just extends so far?
    The given pdf is not valid: it does not integrate to 1.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    The given pdf is not valid: it does not integrate to 1.
    I get one whether by hand or on wolfram alpha...
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  4. #4
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    Quote Originally Posted by xamius View Post
    I get one whether by hand or on wolfram alpha...
    Really? Strange then that I don't.

    My 'by hand' calculation is in agreement with integrate 2/x^3 from 1 to 2000 - Wolfram|Alpha

    Approximately 1 is NOT the same as 1. It is NOT a valid pdf. There is no point in doing the question.
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  5. #5
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    okay I see what you mean. I now see the PDF is (8000000/3999999)*(1/x^3)
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  6. #6
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    Quote Originally Posted by xamius View Post
    okay I see what you mean. I now see the PDF is (8000000/3999999)*(1/x^3)
    So the pdf was not the question? Your pdf was your answer to some other question? It would help if the original question was posted.
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  7. #7
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    well after that correction things turned out looking better for the mean and such. thanks for the help
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